A "mathematically fair bet" is one in which a gambler bets, say, $100 for a 10 percent chance to win $1,000 ($100 = 0.10 × $1,000). Assuming diminishing marginal utility of dollars, this is not a fair bet in terms of utility because

the winnings are reduced

Step-by-step explanation:

Given 10 percent chance to win $1,000 for $100. That is

Gain = $900

Assuming diminishing marginal utility of dollars, when the utility of the gain and the money used for bet are considered, it is discovered that the utility of the $100 used to make the bet is greater than the $900 that you might gain if you win the bet.

this is not a fair bet in terms of utility because the winnings are reduced.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

a

step-by-step explanation:

strong negative correlation